# Airplane Takeoff, Find Thrust

1. Feb 11, 2010

### erok81

1. The problem statement, all variables and given/known data

An Airbus A320 jetliner has a takeoff mass of 75,000 kg. It reaches its takeoff speed of 82 m/s in 35s.

2. Relevant equations

F=ma
V/t=a

3. The attempt at a solution

I am completely lost on this question. I have seen numerous examples on the internet, with the exact problem, but no one has gotten the correct answer. After two hours and 20+ wrong answers I gave up and opted to see the answer. However, I would like to know how it was solved. Here is what I did that got me close to the right answer.

Solved for acceleration indepentant of friction. Which was 82/35 giving me 2.343m/s^2.

I plugged that in for f(thrust)=ma -> (75,000)(2.343) = 175,725 N.

This is too low and doesn't involve rolling friction. From a table in my book I figured rolling friction was 0.020 for rubber on concrete. I then solved for the friction.

m=75,000
g=9.80
f=0.020

F=ma -> F=(75,000)(9.80)(0.020) = 14,700N

Since the thrust will have to include overcoming friction the whole time, I add those two values and get 190,425 N.

This is the only way I can come close to the actual answer. I've done it a bunch of different ways, none were within 20k of the answer.

How should one actually solve this?

The answer given is 190,000N.

2. Feb 11, 2010

### Jebus_Chris

!!!
$$F =/= ma$$
$$F_{net}=ma$$

So expanding Fnet gives us
$$F_t -F_f = ma$$
Plugging everything in gives us a thrust of 190 000 N.

3. Feb 11, 2010

### erok81

Did I have the value for friction right?

Because using my values and your expansion, I get the same answer I had before...

4. Feb 11, 2010

### Jebus_Chris

I would imagine the answer is using two sig figs since all numbers are given with two sig figs.

5. Feb 11, 2010

### erok81

That makes sense, thanks for the help. I'll try the problem again later and see if I remember it.

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